Normalizers and permutational isomorphisms in simply-exponential time

TL;DR

This paper demonstrates that normalizers and permutational isomorphisms of permutation groups can be computed in simply exponential time by leveraging canonical forms, advancing computational group theory methods.

Contribution

It introduces an approach to compute normalizers and permutational isomorphisms in exponential time using canonical forms for permutation groups.

Findings

Normalizers can be computed in simply exponential time.

Permutational isomorphisms can be identified efficiently using canonical forms.

The method advances the understanding of computational complexity in permutation group problems.

Abstract

We show that normalizers and permutational isomorphisms of permutation groups given by generating sets can be computed in time simply exponential in the degree of the groups. The result is obtained by exploiting canonical forms for permutation groups (up to permutational isomorphism).